Improving the DWT-LMS algorithm: boundary filter DWT matrix construction

It has been shown that the discrete wavelet transform (DWT) domain least mean squares (LMS) algorithm increases the rate of convergence with low misadjustment noise and performs better than the discrete cosine transform (DCT) domain and unmodified LMS algorithms. However, the DWT matrix is generally constructed with the assumption of periodic boundary conditions. This circular signal extension technique embeds redundancy into the transform matrix that would seem to be ill suited for the application of transform domain LMS. To circumvent this problem, we introduce boundary filters in the construction of the DWT matrix. This results in an improvement in convergence speed and a reduction in misadjustment error. Numerical examples are presented that support the theory.